1. CSE 102 Introduction to Computer Engineering What is an Algorithm?

2. What is an algorithm? An algorithm is a well-defined procedure that allows the computer to solve a problem.

3. What is an algorithm? Example algorithms: Cooking a dish Making a peanut-butter jelly sandwich Shampooing hair Programming a VCR Making a pie

4. Example Is this an algorithm? Step 1: Wet hair Step 2: Lather Step 3: Rinse Step 4: Repeat Would you manage to wash your hair with this algorithm? How about a robot? Why (not)?

5. Algorithms An algorithm must: be well-ordered and unambiguous, each operation must be effectively computable, terminate

6. Example Problem: Find and print the 100th prime number –A prime number is a whole number not evenly divisible by any other number other than 1 and itself Algorithm (?): 1. Generate a list of all prime numbers n1, n2, n3, … 2. Sort the list in ascending order 3. Print out the 100th element in this list Is this an algorithm?

7. Algorithms An algorithm consists of: the actions to be executed, and the order in which the actions are to be executed

8. Example Problem: Find the sum of the first 5 numbers in a list. Actions: Set the initial value of SUM to 0 Take the first number from the list Add the number to SUM Take the next number from the list Algorithm: 1.Set the initial value of SUM to 0 2.Take the first number from the list 3.Add the number to SUM 4.Take the next number from the list 5.Repeat steps 3-4 five times

9. Pseudocode Pseudocode is an informal language that helps programmers develop algorithms.

10. Example Problem: Find the sum of the first 5 numbers in a list. Pseudocode: 1.SUM ← 0 2.N ← first number in the list 3.SUM ← SUM + N 4.N ← next number in the list 5.Repeat steps 3-4 five times

11. Flowchart Flowchart is a graphical representation of an algorithm.

12. Example Problem: Find the sum of the first 5 numbers in a list. SUM ← 0 N ← first number in the list SUM ← SUM + N N ← next number in the list five times exit True False start

13. Flowchart Flowchart symbols: Sequence structure Selection structure Repetition structure

14. Flowchart Sequence structure SUM ← 0

15. Flowchart Selection structure N>50 TrueFalse

16. Flowchart Repetition structure repeated action condition True False

17. Example Problem: Read the grades of 20 students and print “passed” if the grade is greater than or equal to 50, otherwise print “failed”. COUNT ← 0 Read grade COUNT=20 exit True False grade >= 50 True False Print “passed”Print “failed” COUNT ← COUNT+1

18. Variables Variable –A named memory location that can store a value –Think of it as a box into which you can store a value, and from which you can retrieve a value Examples: Example of operations Set the value of i to 3 Set the value of M to i*3 + 12 Set the value of i to i+10 i M

19. A model for visualizing an algorithm Algorithm Variables Operations An algorithm consists of operations that involve variables

20. Primitive operations Get input from user –Get the value of x from user Assign values to variables using basic arithmetic operations –Set the value of x to 3 –Set the value of y to x/10 –Set the value of z to x +25 Print output to user –Print the value of y, z to the user

21. Example Problem: For any three numbers input by the user, compute their sum and average, and output them Example of algorithm in pseudocode: Variables: a, b, c, sum, avg 1.Get the values of a, b, c from user 2.Set avg to (a+b+c)/3 3.Set sum to (a+b+c) 4.Print sum and avg

22. Example 2 Problem: Given any value of radius from the user, compute and print the circumference of a circle with that radius Algorithm in pseudocode: variables: r, c 1. Get the value of r from user 2. Set c to 2 * pi * r 3. Print “The circumference of your circle is “ c

23. Basic operations –Read the input from user Get x Get a, b, c –Print the output to the user Print x Print “Your mileage is ” x –Cary out basic arithmetical computations Set x to 10 Set y to x*x/3

24. Conditional statements Specify a statement that may or may not be done: if then else Example if the value of A is greater than 5 then set the value of B to 1 else set the value of B to 0

25. Loop statements specify a group of statements that may be done several times (repeated): repeat until How does this work? –Condition is evaluated –If it is true than the loop terminates and the next instruction to be executed will be the instruction immediately following the loop –If it is false, then the algorithm executes the in order, one by one

26. Example Variables: count Step 1: set count to 1 Step 2: repeat step 3 to step 5 until count is > 10 Step 3: set square to count *count Step 4: print value of square and value of count Step 5: add 1 to count Step 6: end What does this algorithm do? Note: indentation –Not necessary, but makes reading/understanding algorithms easier

27. Pseudocode examples Equivalent: –Set the value of a to 1 –Set a to 1 –a=1 –a←1 Equivalent: –Add 1 to count –Set count to count + 1 –Increment the value of count by 1 –count = count + 1 –count ← count + 1 Writing in pseudocode gives you the freedom to choose any of these!

28. Incorrect –Set 1 to a –Add a + b (what do you do with the result?) –Set a+b +3 Note: not the same –set a to b –set b to a Example: what is the output of the following algorithms?set a to 2set b to 4 set a to bset b to aprint a, b

29. A model for visualizing an algorithm’s behavior Algorithm Computer Input (keyboard) Output (screen) Variables

30. Designing Algorithms: A Methodology 1.Read the problem, identifying the input and the output. 2.What variables are needed? 3.What computations are required to achieve the output? 4.Usually, the first steps in your algorithm bring input values to the variables. 5.Usually, the last steps display the output 6.So, the middle steps will do the computation. 7.If the process is to be repeated, add loops.

31. More algorithms Write algorithms to find –the largest number in a list of numbers (and the position where it occurs) –the smallest number in a list of numbers (and the position where it occurs) –the range of a list of numbers Range= largest - smallest –the average of a list of numbers –the sum of a list of numbers